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The algorithm for adjacent vertex distinguishing proper edge coloring of graphs

2015
*
Discrete Mathematics, Algorithms and Applications (DMAA)
*

An adjacent

doi:10.1142/s1793830915500445
fatcat:mlbznz4mfbar3mztxhtaauk6pu
*vertex**distinguishing**proper**edge**coloring*of a graph G is a*proper**edge**coloring*of G such that no pair of adjacent vertices meet the same set of*colors*. ... The minimum number of*colors*is called adjacent*vertex**distinguishing**proper**edge*chromatic number of G. ... proof on conjecture of adjacent*vertex**distinguishing**proper**edge**coloring*. ...##
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On Twin Edge Colorings of d Infinite Paths

2017
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DEStech Transactions on Engineering and Technology Research
*

Let σ be a

doi:10.12783/dtetr/oect2017/16125
fatcat:b73x3slme5bkzgliz5vxo2ptfi
*proper**edge**coloring*of a connected graph G of order at least 3, where the If σ can induce a*proper**vertex**coloring*of G , then σ is called a twin*edge*k-*coloring*of G . ... The minimum number of*colors*for which G has a twin*edge**coloring*is called the twin chromatic index of G . ... Recently, an adjacent*vertex**distinguishing**edge*-*coloring*[1] of a simple graph G is a*proper**edge*-*coloring*of G such that no pair of adjacent vertices has the same set of*colors*. ...##
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Color-blind index in graphs of very low degree

2017
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Discrete Applied Mathematics
*

When c^* induces a

doi:10.1016/j.dam.2017.03.006
fatcat:wk6gbsunsnh5tfanmndagzmfqy
*proper**vertex**coloring*, that is, c^*(u)≠ c^*(v) for every*edge*uv in G, we say that c is*color*-blind*distinguishing*. ... Let c:E(G)→ [k] be an*edge*-*coloring*of a graph G, not necessarily*proper*. For each*vertex*v, let c̅(v)=(a_1,...,a_k), where a_i is the number of*edges*incident to v with*color*i. ... The*edge*-*coloring*c is neighbor*distinguishing*ifc is a*proper**vertex**coloring*of the vertices of G. ...##
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Concise proofs for adjacent vertex-distinguishing total colorings

2009
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Discrete Mathematics
*

We say that f is an adjacent

doi:10.1016/j.disc.2008.06.002
fatcat:i3yr6edw3rfjnjeavjwofi5xdi
*vertex*-*distinguishing*total*coloring*if for any two adjacent vertices, the set of*colors*appearing on the*vertex*and incident*edges*are different. ... Let G = (V , E) be a graph and f : (V ∪E) → [k] be a*proper*total k-*coloring*of G. ... This is an AVDTC because it is clearly*proper*and the*color*sets of adjacent vertices are*distinguished*by their*vertex**color*. ...##
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A PROPER TOTAL COLORING DISTINGUISHING ADJACENT VERTICES BY SUMS OF SOME PRODUCT GRAPHS

2015
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Communications of the Korean Mathematical Society
*

In this article, we consider a

doi:10.4134/ckms.2015.30.1.045
fatcat:5gos3fpfffemxos44xeiutifvm
*proper*total*coloring**distinguishes*adjacent vertices by sums, if every two adjacent vertices have different total sum of*colors*of the*edges*incident to the*vertex*and the ...*color*of the*vertex*. ... Woźniak [15] first introduced that a*proper*total*coloring*of Γ is a*proper*total*colorings**distinguishing*adjacent vertices by sums if for a*vertex*v ∈ V (Γ), the total sum of*colors*of the*edges*incident ...##
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Smarandachely Adjacent Vertex Distinguishing Edge Coloring of Some Graphs

2019
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Journal of Physics, Conference Series
*

A Series of new

doi:10.1088/1742-6596/1168/6/062022
fatcat:zzig53pxnjbsbm3a2iosn4lrpm
*coloring*problems (such as*vertex**distinguishing**edge**coloring*,*vertex**distinguishing*total*coloring*, adjacent*vertex**distinguishing**edge**coloring*, smarandachely adjacent*vertex**distinguishing*... At present, there are relatively few articles on smarandachely adjacent*vertex**distinguishing**edge**coloring*. ... Then a k −*proper**edge**coloring*f of a graph G is called a smrandachely adjacent*vertex**distinguishing**edge**coloring*if for all adjacent*vertex*u and v , we have ( ) Evidently graph with one-degree -*vertex*...##
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Neighbor sum distinguishing total coloring of 2-degenerate graphs

2016
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Journal of combinatorial optimization
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A

doi:10.1007/s10878-016-0053-5
fatcat:h6zuvj4i7fab7iq4pfwederzom
*proper*k-total*coloring*of G is called neighbor sum*distinguishing*if f (u) = f (v) for each*edge*uv ∈ E(G). ... Let f (v) denote the sum of the*colors*on the*edges*incident with v and the*color*on*vertex*v. ... A*proper*k-total*coloring*φ of G is called a neighbor sum (set)*distinguishing*k-total*coloring*if f (u) = f (v) (S(u) = S(v)) for each*edge*uv ∈ E(G), where f (v) (S(v)) is the sum (set) of*colors*on ...##
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Optimal Adjacent Vertex-Distinguishing Edge-Colorings of Circulant Graphs
[article]

2022
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arXiv
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pre-print

A k-

arXiv:2004.12822v4
fatcat:bjnfyoej7vh43jwidiwtnma3vm
*proper**edge*-*coloring*of a graph G is called adjacent*vertex*-*distinguishing*if any two adjacent vertices are*distinguished*by the set of*colors*appearing in the*edges*incident to each*vertex*. ... The smallest value k for which G admits such*coloring*is denoted by χ'_a(G). We prove that χ'_a(G) = 2R + 1 for most circulant graphs C_n([1, R]). ... Some interest has been shown in non-*proper*adjacent*vertex*-*distinguishing**edge*-*colorings*. ...##
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On the Vertex-Distinguishing Edge Chromatic Number of 𝐏𝐦 ∨ 𝐂𝐧

2017
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DEStech Transactions on Engineering and Technology Research
*

In this paper, we present the

doi:10.12783/dtetr/icamm2016/7349
fatcat:gcxlenvdl5an5g3bfyigg4bd5e
*edge**coloring*of join-graphs about path and cycle, and gain the*vertex*-*distinguishing**edge*chromatic number of ∨ . ... A*proper**edge**coloring*of graph G is called equitable adjacent strong*edge**coloring*if*colored*sets from every two adjacent vertices incident*edge*are different, and the number of*edges*in any two*color*... In [5] introduced the*vertex*-*distinguishing**edge**coloring*of graph, and give the correspondence conjecture. ...##
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On the Total-Neighbor-Distinguishing Index by Sums

2013
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Graphs and Combinatorics
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We consider a

doi:10.1007/s00373-013-1399-4
fatcat:pb6os3u2ibeu5eqnc2lht6vucu
*proper**coloring*c of*edges*and vertices in a simple graph and the sum f (v) of*colors*of all the*edges*incident to v and the*color*of a*vertex*v. ... We conjecture that + 3*colors*suffice to*distinguish*adjacent vertices in any simple graph. ... Recently, some other authors in [3] considered a*proper**coloring*of*edges**distinguishing*adjacent vertices by sums. ...##
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On the adjacent vertex distinguishing total coloring numbers of graphs with Δ=3

2008
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Discrete Mathematics
*

An adjacent

doi:10.1016/j.disc.2007.07.091
fatcat:oefh3wargnahlamsxxorkd667y
*vertex**distinguishing*total-*coloring*of a simple graph G is a*proper*total-*coloring*of G such that no pair of adjacent vertices meets the same set of*colors*. ... The minimum number of*colors*a (G) required to give G an adjacent*vertex**distinguishing*total-*coloring*is studied. We proved a (G) 6 for graphs with maximum degree (G) = 3 in this paper. ... From [3] we know that the*vertex**distinguishing**proper**edge**coloring*number of G is at most 3s + t + 2. ...##
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L-factors and adjacent vertex-distinguishing edge-weighting
[article]

2010
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arXiv
*
pre-print

Using these results, we investigate

arXiv:1007.1295v1
fatcat:mwfmqzmowzgwxjm44ixbyy63be
*edge*-weighting problem. In particular, we prove that every 4-*colorable*graph admits a*vertex*-*coloring*4-*edge*-weighting. ... An*edge*weighting problem of a graph G is an assignment of an integer weight to each*edge*e. Based on*edge*weighting problem, several types of*vertex*-*coloring*problems are put forward. ... The*coloring*is*proper*if no two adjacent vertices share the same*color*. A graph G is k-*colorable*if G has a*proper*k-*vertex**coloring*. ...##
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Probing Graph Proper Total Colorings With Additional Constrained Conditions
[article]

2015
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arXiv
*
pre-print

Graph

arXiv:1601.00883v1
fatcat:3tm4iea53bhadl7sbw6wkj3e2q
*proper*total*colorings*with additional constrained conditions have been investigated intensively in the last decade year. ... In this article some new graph*proper*total*colorings*with additional constrained conditions are defined, and approximations to the chromatic numbers of these*colorings*are researched, as well as some ... In the article [6] , Burris and Schelp introduce that a*proper**edge*-*coloring*of a simple graph G is called a*vertex**distinguishing**edge*-*coloring*(vdec) if for any two distinct vertices u and v of G, the ...##
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The Vertex-Distinguishing Edge Coloring of 𝑷𝒎⋁𝑲𝒏 and 𝑪𝒎 ∨ 𝑲𝒏

2017
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DEStech Transactions on Engineering and Technology Research
*

In this paper, we obtain

doi:10.12783/dtetr/icamm2016/7350
fatcat:5nwgjjowjffx7lfnuqerm2tznq
*vertex*-*distinguishing**edge**coloring*of ∨ and ∨ . ... A*proper**edge**coloring*of graph G is called equitable adjacent strong*edge**coloring*if*colored*sets from every two adjacent vertices incident*edge*are different, and the number of*edges*in any two*color*... In [5] introduced the*vertex*-*distinguishing**edge**coloring*of graph, and give the correspondence conjecture. ...##
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A note on the vertex-distinguishing proper coloring of graphs with large minimum degree

2001
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Discrete Mathematics
*

We prove that the number of

doi:10.1016/s0012-365x(00)00428-3
fatcat:qmqyjilj3rfmtbxl3v2b4uzzwy
*colors*required to properly*color*the*edges*of a graph of order n and (G) ¿ n=3 in such a way that any two vertices are incident with di erent sets of*colors*is at most (G) ... The*coloring*f is*proper*if no two adjacent*edges*are assigned the same*color*and*vertex*-*distinguishing**proper*(VDP)*coloring*if it is*proper*and F(u) = F(v) for any two distinct vertices u; v. ... The minimum number of*colors*required to ÿnd a VDP*coloring*of a graph G without isolated*edges*and with at most one isolated*vertex*is called the*vertex*-*distinguishing**proper**edge*-*coloring*number and ...
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